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some more lemmas

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Burkhart Wolff 2024-04-04 10:08:41 +02:00
parent 0bf21336f1
commit dee3b47d06
1 changed files with 12 additions and 0 deletions
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Isabelle_DOF/ontologies/technical_report/technical_report.thy
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@ -135,7 +135,12 @@ notation Atom ("\<lfloor>_\<rfloor>" 65)
lemma regexp_seq_mono:
"Lang(a) \<subseteq> Lang (a') \<Longrightarrow> Lang(b) \<subseteq> Lang (b') \<Longrightarrow> Lang(a ~~ b) \<subseteq> Lang(a' ~~ b')" by auto
lemma regexp_alt_mono :"Lang(a) \<subseteq> Lang (a') \<Longrightarrow> Lang(a || b) \<subseteq> Lang(a' || b)" by auto
lemma regexp_alt_commute : "Lang(a || b) = Lang(b || a)" by auto
lemma regexp_unit_right : "Lang (a) = Lang (a ~~ One) " by simp
lemma regexp_unit_left : "Lang (a) = Lang (One ~~ a) " by simp
lemma opt_star_incl :"Lang (opt a) \<subseteq> Lang (Star a)" by (simp add: opt_def subset_iff)
@ -152,6 +157,13 @@ lemma seq_cancel_opt : "Lang (a) \<subseteq> Lang (c) \<Longrightarrow> Lang (a)
lemma seq_cancel_Star : "Lang (a) \<subseteq> Lang (c) \<Longrightarrow> Lang (a) \<subseteq> Lang (Star b ~~ c)"
by auto
lemma mono_Star : "Lang (a) \<subseteq> Lang (b) \<Longrightarrow> Lang (Star a) \<subseteq> Lang (Star b)"
by(auto)(metis in_star_iff_concat order.trans)
lemma mono_rep1_star:"Lang (a) \<subseteq> Lang (b) \<Longrightarrow> Lang (rep1 a) \<subseteq> Lang (Star b)"
using mono_Star rep1_star_incl by blast
text\<open>Not a terribly deep theorem, but an interesting property of consistency between
ontologies - so, a lemma that shouldn't break if the involved ontologies were changed:
the structural language of articles should be included in the structural language of